Question

A wire, of length L = 4.9 mm, on a circuit board carries a current of I = 2.73 uA in the j direction. A nearby circuit element generates a magnetic field in the vicinity of the wire of B=B,i + B, j + B k, where Bx = 2.8 G, B, = 3.3 G, and B, = 2.9 G. A 17% Part (a) Calculate the magnitude of the magnetic field B. in gauss, in the vicinity of the wire due to the circuit element. Grade Summary B= Deductions 0% Potential 100% HOME E sino cos tant cotano asino acoso atan acotan sinh cosh tanh cotanh() Degrees O Radians ( 7 8 4 5 * 1 2 + - 0 NO BACKSPACE 9 6 3 Submissions Attempts remaining: 10 (0% per attempt) detailed view = END CLEAR Submit Hint Feedback I give up! Hints: 3% deduction per hint. Hints remaining: 2 Feedback: 3% deduction per feedback. Feedba A 17% Part (b) Calculate the i component of the magnetic force Fr. in newtons, exerted on the wire by the magnetic field due to the circuit element. A 17% Part (c) Calculate the j component of the magnetic force Fy, in newtons, exerted on the wire by the magnetic field due to the circuit element. A 17% Part (d) Calculate the k component of the magnetic force Fz. in newtons, exerted on the wire by the magnetic field due to the circuit element. A 17% Part (e) Calculate the magnitude of the magnetic force F. in newtons, exerted on the wire by the magnetic field due to the circuit element. A 17% Part (f) If you simply multiply the current, the length, and the magnetic field strength ILB, (in appropriate units), you will find that this results in a larger calculated force larger than the answer to part (e). Which of the following scenarios would result in the maximum force exerted on the current carrying wire?

Answer 1

The magnitude of the magnetic field B in the vicinity of the wire due to the circuit element is 5.25 G. The i, j, and k components of the magnetic force exerted on the wire are approximately 7.64 * 10^-6 N, 8.99 * 10^-6 N, and 7.92 * 10^-6 N, respectively. The magnitude of the magnetic force exerted on the wire is approximately 1.192 * 10^-5 N.

Step-by-step explanation:

The magnitude of the magnetic field B in the vicinity of the wire due to the circuit element can be calculated using the formula B = sqrt(Bx^2 + By^2 + Bz^2), where Bx = 2.8 G, By = 3.3 G, and Bz = 2.9 G. Plugging in the given values, we get B = sqrt((2.8)^2 + (3.3)^2 + (2.9)^2) = 5.25 G.

The i component of the magnetic force Fr exerted on the wire by the magnetic field can be calculated using the formula Fr = I * Bx, where I = 2.73 uA and Bx = 2.8 G. Plugging in the values, we get Fr = (2.73 * 10^-6 A) * (2.8 G) = 7.64 * 10^-6 N.

Similarly, the j component of the magnetic force Fy can be calculated using the formula Fy = I * By, where I = 2.73 uA and By = 3.3 G. Plugging in the values, we get Fy = (2.73 * 10^-6 A) * (3.3 G) = 8.99 * 10^-6 N.

The k component of the magnetic force Fz can be calculated using the formula Fz = I * Bz, where I = 2.73 uA and Bz = 2.9 G. Plugging in the values, we get Fz = (2.73 * 10^-6 A) * (2.9 G) = 7.92 * 10^-6 N.

The magnitude of the magnetic force F exerted on the wire by the magnetic field can be calculated using the formula F = sqrt(Fr^2 + Fy^2 + Fz^2), where Fr = 7.64 * 10^-6 N, Fy = 8.99 * 10^-6 N, and Fz = 7.92 * 10^-6 N. Plugging in the given values, we get F = sqrt((7.64 * 10^-6)^2 + (8.99 * 10^-6)^2 + (7.92 * 10^-6)^2) = 1.192 * 10^-5 N.